Applied functional analysis. (English) Zbl 0461.46001

Ellis Horwood Series in Mathematics and its Applications. Chichester: Ellis Horwood Limited, Publishers. New York etc.: Halsted Press: a division of John Wiley & Sons. 386 p. £25.00 (1981).


46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46F05 Topological linear spaces of test functions, distributions and ultradistributions
46B03 Isomorphic theory (including renorming) of Banach spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
46E15 Banach spaces of continuous, differentiable or analytic functions
46E20 Hilbert spaces of continuous, differentiable or analytic functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46F10 Operations with distributions and generalized functions
46F12 Integral transforms in distribution spaces
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A10 Spectrum, resolvent
47A53 (Semi-) Fredholm operators; index theories
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47B38 Linear operators on function spaces (general)
47D03 Groups and semigroups of linear operators
47E05 General theory of ordinary differential operators
47F05 General theory of partial differential operators
47Gxx Integral, integro-differential, and pseudodifferential operators
47H10 Fixed-point theorems
47J05 Equations involving nonlinear operators (general)
47J25 Iterative procedures involving nonlinear operators
49R50 Variational methods for eigenvalues of operators (MSC2000)
34A30 Linear ordinary differential equations and systems
34A35 Ordinary differential equations of infinite order
34L99 Ordinary differential operators
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D99 Stability theory for ordinary differential equations
34E99 Asymptotic theory for ordinary differential equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A08 Fundamental solutions to PDEs
35A15 Variational methods applied to PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35B32 Bifurcations in context of PDEs
35B35 Stability in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35K05 Heat equation
35L05 Wave equation
35J15 Second-order elliptic equations
35J20 Variational methods for second-order elliptic equations
35J30 Higher-order elliptic equations
35J35 Variational methods for higher-order elliptic equations
35P05 General topics in linear spectral theory for PDEs
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
42A20 Convergence and absolute convergence of Fourier and trigonometric series
42A65 Completeness of sets of functions in one variable harmonic analysis
42B05 Fourier series and coefficients in several variables
45B05 Fredholm integral equations
45C05 Eigenvalue problems for integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
70J25 Stability for problems in linear vibration theory
70K20 Stability for nonlinear problems in mechanics
70K30 Nonlinear resonances for nonlinear problems in mechanics
37G99 Local and nonlocal bifurcation theory for dynamical systems
76R99 Diffusion and convection
76U05 General theory of rotating fluids